Pearson+ LogoPearson+ Logo
Start typing, then use the up and down arrows to select an option from the list.

Find Magnetic Field By Two Concentric Loops

Patrick Ford
Was this helpful?
Hey, guys. So let's check out this example. So here we have to wire loops that are concentric Lee arranged meaning concentric means one circle inside of the other, right, with a common middle eso It's shown below, and the inner wire has diameter four. Now, real quick in physics, remember, we almost never used diameter were almost always use radius. I'm gonna right away. Change this. Um, instead of writing diameter one, I'm gonna radius one and radius is half of the diameter. So that's 2 m in the clockwise currents of five. So that's the inner one here, which is blue, and it's got a clockwise currents of five amps. So I'm gonna put here five amps s o I one is five amps and radius one is m and then the red one is counter clockwise counterclockwise, which is this way, and it's got a current of seven amps in that direction. So I can write that I to is 7 a.m. and R. Two is the diameter, which is six. It's actually the radius, which is gonna be three half of the diameter. Okay, and we're looking for is the net the net magnetic field at the center. Remember what you have a current when you have a loop current. So you have a loop of wire with current going through it. It's gonna produce a magnetic field through the center of the ring, either in or out. Right. And we have two rings with the same common center. So both rings or both loops will be contributing. Um, to this here, which is why we're talking about the next magnetic fields because it's gonna be a contribution of both. It's gonna be a combination of both. So let's find those two numbers B one and B two, and the equation is mu knots. I divided by two big art where big R is the radius. And we have all of these numbers. Um, it's I won, since it's B one and it's our one since it's B one, right? So once go, go with once. So this is four pi times 10 to the negative seven and the current is a five, and the radius here is a true okay. And if you plug this into your calculator, you're gonna get that this is 15 7 or actually should say, um, 1.57 times, 10 to the negative. Six times 10 to the negative six. Okay. And if you do this with B two, it's very similar. Just the numbers are a little bit different. So instead of a five up here, you're gonna have a seven. And instead of a two over here, you're gonna have a three, okay? And if you do this, you get 1.67 times 10 times 10 to the negative six. Okay, now let's talk about direction. Let's talk about direction to find direction. I'm gonna use the right hand rule. So first, let's look at the blue inner circle. The blue inner circle is not going this direction, but it's actually going in this direction, right? It's going clockwise like this. If you do this, your thumb points away from you, which is into the page. Which means that the first one, the inner one, is going to go into the page and the other one is in the opposite direction, so it must go in the opposite direction. So this is going to be out of the page. And if you want to confirm, uh, if you want to confirm you could just use again your hand and grab the outer wire goes this way right this way. And look, my thumb is not pointing my face, which is out of the page and towards meat because these guys were going in different directions. We can't just add their magnitudes. In fact, we have to subtract. And the way to do this is you start with the bigger one and then you're gonna say, Hey, this guy is the bigger one. So it's the winner. This one wins, right? It's kinda like a tug of war ones pulling this way, the other ones pulling the other way. This one wins. So the next magnetic field is going to be a winner minus loser. So 1.67 times 10 to the negative six minus 1.57 times 10 to the negative six. This is actually just a matter of subtracting this minus this because it's got the same power of 10. So this is going to be 0.1 times 10 to the negative 60.1 Time center. Negative six. But we can multiply despite 10 and then we have to divide this by 10. We multiply this by 10 so we get one times instead of one. And if we multiply here, we have to divide here. So it's fair. So it's so we're not actually changing the number, and this divided by 10 is 1 10 to the negative seven. By the way, you could also have answered just 10 to negative seven. But that's that. So this is one times 10 to the negative seven. Tesla, uh, and in what direction? It's going out of the page because that was the winning direction of the two. Okay, so that's it's That's one way you could do it another way. You could have done this. You could have just assigned signs, and you could have said, Hey, um, into the page into the page is like this right away from you with my thumb and my fingers are currently in the clockwise direction. Clockwise is usually negative, so we can say that into the page is negative and out of the pages positive, right? So then you would have done this with numbers and you would have gotten the same results anyway cope so you can think of winner the big one minus loser, the smallest one and then the winner dictates the direction, the next direction. Or you could just assign positives and negatives on Do the math. That's it for this one. Let's get going.